Photoelectron spectra of gas-phase molecules display sharp vibrational structure. The envelope of the spectrum is determined by the Franck-Condon factor. On the other hand, photoelectron spectra of the same molecules, adsorbed or condensed onto metal surfaces show a broad band whose shape resembles the gas-phase Franck-Condon envelope but with no sharp structure. The smearing out of the vibrational structure is usually attributed to lifetime effects or site inhomogeneities. A new mechanism involving intrinsic phonon sidebands in photoemission from condensed molecules is suggested and the details of the theory are worked out. Experimental ultraviolet photoelectron spectra from condensed CO are considered in the light of this theory.